General Cohomology Theory and K-Theory
These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences.
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KTheory the Chern Character and the Hopf
Appendix On the Construction of Cohomology Theories
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abelian groups Adams additional algebraic topology apply associated assume axiom called Chapter Chern character coefficients cohomology theory commutative complex complex vector component conclude connected Consider construction correspondence course defined definition denote described diagram dimension direct limit EC(X element equivalence exact couple example exists extend fact factor Fibre filtration finite follows function functor give given graded hand Hence hº(x homology homomorphism homotopy Hopf invariant hypothesis induced integer isomorphism K-theory Lemma look monomorphism Moreover morphism n-bundle natural transformation notes Notice observe obtained operations ordinary pair Proof prove pullback r+s=q Recall reduced respectively restriction satisfies shows space spectral sequence spectrum splits stable structure subgroup sufficient suppose suspension Theorem theory h topology trivial unique universal vector bundle vector space verify write